[Paper Review] Deconvolutional Networks on Graph Data

Jia Li, Jiajin Li+4 more|arXiv (Cornell University)|Oct 29, 2021

Advanced Graph Neural Networks49 references7 citations

TL;DR

This paper proposes Graph Deconvolutional Networks (GDN), a method to reconstruct original graph signals from representations smoothed by Graph Convolutional Networks (GCNs). By combining inverse spectral filtering with wavelet-based denoising, GDN mitigates noise amplification from direct deconvolution, achieving state-of-the-art performance in graph feature imputation and structure generation tasks.

ABSTRACT

In this paper, we consider an inverse problem in graph learning domain -- ``given the graph representations smoothed by Graph Convolutional Network (GCN), how can we reconstruct the input graph signal?" We propose Graph Deconvolutional Network (GDN) and motivate the design of GDN via a combination of inverse filters in spectral domain and de-noising layers in wavelet domain, as the inverse operation results in a high frequency amplifier and may amplify the noise. We demonstrate the effectiveness of the proposed method on several tasks including graph feature imputation and graph structure generation.

Motivation & Objective

• To address the inverse problem of recovering original graph signals from GCN-smoothed representations.
• To overcome the inherent noise amplification in direct deconvolution of GCN-processed signals.
• To develop a symmetric encoder-decoder framework for graph autoencoders using GDN as a learnable decoder.
• To improve performance in graph feature imputation and graph structure generation tasks.
• To provide a principled design for graph deconvolution by analyzing spectral inverse operations and noise propagation.

Proposed method

• Proposes a spectral-wavelet GDN that applies inverse filters in the spectral domain to reverse GCN smoothing.
• Uses Maclaurin series approximation to efficiently compute inverse filters and wavelet kernels without explicit eigen-decomposition.
• Introduces wavelet-based denoising to suppress high-frequency noise amplified by inverse filtering.
• Employs a symmetric graph autoencoder (GAE) framework with GCN encoder and GDN decoder for end-to-end training.
• Applies the GDN module as a plug-in decoder in variational graph autoencoders (e.g., VGAE, Graphite) to enhance generation quality.
• Leverages the spectral response of GCN as a low-pass filter (g_c(λ) = 1 - λ) to inform the design of the inverse filter g_d(λ) = 1 / (1 - λ).

Experimental results

Research questions

• RQ1 Can we effectively reconstruct original graph signals from GCN-smoothed representations?
• RQ2 How can we mitigate noise amplification caused by the inverse filtering operation in graph deconvolution?
• RQ3 Can a spectral-wavelet hybrid design improve signal recovery over direct inverse filtering?
• RQ4 Does integrating GDN into graph autoencoders enhance performance in feature imputation and structure generation?
• RQ5 To what extent does GDN improve existing generative models like VGAE and Graphite?

Key findings

• The proposed GAE with GDN decoder outperforms state-of-the-art methods on six benchmark datasets for graph feature imputation.
• On the MUTAG dataset, GDN improves the AP score of Graphite by 16.1% in graph structure generation.
• On the PTC-MR dataset, GDN enhances the AUC score of Graphite by 20.9%.
• In the VGAE framework, GDN increases the log-likelihood score (log p(A|Z)) by 0.029 on the ZINC dataset.
• The spectral-wavelet GDN design effectively suppresses noise amplification, outperforming naive inverse filtering.
• The method demonstrates strong generalization, improving performance across diverse graph learning tasks with minimal architectural modification.